Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}3x+4y &= 1 \\ -x-y &= 1\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-y = x+1$ Divide both sides by $-1$ to isolate $y$ $y = {-x - 1}$ Substitute this expression for $y$ in the first equation. $3x+4({-x - 1}) = 1$ $3x - 4x - 4 = 1$ Simplify by combining terms, then solve for $x$ $-1x - 4 = 1$ $-1x = 5$ $x = -5$ Substitute $-5$ for $x$ back into the top equation. $3( -5)+4y = 1$ $-15+4y = 1$ $4y = 16$ $y = 4$ The solution is $\enspace x = -5, \enspace y = 4$.